502- 2 Investment Risk and Return

Question 1

Explain the following terms related to the measurement of investment risk: total risk

Answer 1

The uncertainty that an investment will deliver its expected return; measured by a security’s standard deviation.

Question 2

Explain the following terms related to the measurement of investment risk: standard deviation

Answer 2

The degree to which an investment’s returns can be expected to vary from its mean return.

Question 3

Explain the following terms related to the measurement of investment risk: covariance

Answer 3

The tendency of two assets to move together or apart.

Question 4

Explain the following terms related to the measurement of investment risk: correlation coefficient

Answer 4

A standardized version of covariance.

Question 5

Explain the following terms related to the measurement of investment risk: beta

Answer 5

A measure of a security’s volatility with respect to an index against which the stock is measured.

Question 6

What is endogenous risk, and why must advisers be aware of it?

Answer 6

Endogenous risk is a risk found within the financial system, and occurs when there is a shock (or panic), which then spreads and is amplified within the system. As advisers saw with the 2008 financial crisis, this type of risk is extremely harmful to investors, and should be taken into account by the adviser when constructing portfolios.

Question 7

Unsystematic risk can be diversified away by holding approximately how many securities?

Answer 7

Approximately 10 to 15 securities are required to diversify away unsystematic risk. (I.E.- 15 Large Cap positions)

Question 8

Explain each of the following types of systematic risk: market risk

Answer 8

Market risk is caused by investor reaction to tangible and intangible factors independent of a particular security or property. It is the effect of a movement of the market overall.

Question 9

Explain each of the following types of systematic risk: interest rate risk

Answer 9

Interest rate risk is the negative effect on the prices of fixed- income securities caused by increases in the general level of interest rates

Question 10

Explain each of the following types of systematic risk: reinvestment risk

Answer 10

Reinvestment risk, sometimes called reinvestment rate risk, is the problem of receiving periodic payments or principal and being able to reinvest them only at lower rates.

Question 11

Explain each of the following types of systematic risk: purchasing power risk

Answer 11

Purchasing power risk, or inflation risk, is the risk associated with the loss of purchasing power due to a rise in the general level of prices.

Question 12

Explain each of the following types of systematic risk: exchange rate risk

Answer 12

Exchange rate risk, or currency risk, is the uncertainty associated with changes in the value of foreign currencies. Relative to the U.S. dollar, it is the risk that converting a foreign currency into U.S. dollars provides fewer dollars than previously held.

Question 13

Explain each of the following types of unsystematic risk: business risk

Answer 13

Business risk is related to the uncertainty associated with a particular investment. It most often is concerned with the degree of uncertainty associated with a company’s earnings and its ability to pay dividends or interest to investors.

Question 14

Explain each of the following types of unsystematic risk: financial risk

Answer 14

Financial risk is the risk associated with the degree to which debt is used by a company to finance a particular firm or property. The higher the level of debt, the higher the financial risk. An entity with no debt has no financial risk.

Question 15

Explain each of the following types of unsystematic risk: default risk

Answer 15

Default risk is the chance of the issuer defaulting on its financial obligations, resulting in investors not receiving some or all of their principal.

Question 16

Explain each of the following types of unsystematic risk: credit risk

Answer 16

Credit risk is the degree of an issuer’s default risk that is reflected in its credit ratings assigned by major credit rating companies. An unanticipated lowering of the credit rating of an issuer’s debt can cause the price of its debt to drop significantly in response.

Question 17

Explain each of the following types of unsystematic risk: liquidity and marketability risk

Answer 17

Liquidity risk most often is described as the degree of uncertainty associated with the ability to sell an investment quickly without loss of principal. An alternative definition is the chance of capital loss. Marketability risk is the risk that there is no active market for an investment.

Question 18

Explain each of the following types of unsystematic risk: call risk

Answer 18

Call risk is the possibility that the issuer will call in the debt issue prior to maturity, resulting in reinvesting the proceeds at lower rates of interest.

Question 19

Explain each of the following types of unsystematic risk: event risk

Answer 19

Event risk is the possibility that an unanticipated event or action will affect an issuer’s securities in a significant manner.

Question 20

Explain each of the following types of unsystematic risk: tax risk

Answer 20

Tax risk is the risk associated with the uncertainty of an adverse outcome due to the interpretation of tax laws and regulations.

Question 21

Explain each of the following types of unsystematic risk: investment manager risk

Answer 21

This risk is associated with actions of the investment manager that could adversely impact one’s investment in the fund he or she is managing.

Question 22

Explain each of the following types of unsystematic risk: political risk

Answer 22

Political risk is the uncertainty caused by the possibility of adverse political events occurring in a country.

Question 23

Identify the type of investment risk posed by the following situations: Inflation is expected to rise over the next year.

Answer 23

Purchasing power risk

Question 24

Identify the type of investment risk posed by the following situations: Exxon Mobil decides to issue bonds instead of stock to finance a new tanker fleet.

Answer 24

Financial risk

Question 25

Identify the type of investment risk posed by the following situations: The Fed has decided to increase short-term interest rates to fight increased inflation.

Answer 25

Interest rate risk

Question 26

Identify the type of investment risk posed by the following situations: United Airlines fights discount carriers by lowering its fares across the country.

Answer 26

Business risk

Question 27

Identify the type of investment risk posed by the following situations: Interest rates have declined over the past year.

Answer 27

Reinvestment risk

Question 28

Identify the type of investment risk posed by the following situations: The overvalued stock market has finally fallen 15% over the past four months.

Answer 28

Market risk

Question 29

Identify the type of investment risk posed by the following situations:The value of your investment in Sony has risen 20% during the past year; during the same period, the yen has weakened against the dollar, causing the total return on the Sony investment to be only 10%.

Answer 29

Exchange rate risk

Question 30

Steve Jenkins owns two stocks: PTV Inc. and SLK Corp. He owns 100 shares of PTV Inc. with a current market value of $5,250, and 150 shares of SLK Corp., with a current market value of $1,750. Steve expects returns of 20% and 14%, respectively, on his investments. What is the overall weighted-average expected return on Steve’s portfolio? (Set your calculator to four decimal places. Also, use the calculator function keys to solve the problem more quickly.)

Answer 30

20 INPUT
5250 Σ+
14 INPUT
1750 Σ+
SHIFT ⎯xw (6 key)
Rate of return = 18.50%

Question 31

Christa Pate owns unimproved land with a current market value of $175,000, 50 NLR convertible bonds with a current market value of $48,500, and 1,000 shares of MPT stock with a current market value of $72,500. Christa expects returns of 14%, 21%, and 9%, respectively, on her investments. What is the overall weighted-average expected return on Christa’s portfolio? (Set your calculator to four decimal places. Also, use the calculator function keys to solve the problem more quickly.)

Answer 31

14 INPUT
175,000 Σ+
21 INPUT
48,500 Σ+
9 INPUT
72,500 Σ+
SHIFT ⎯xw (6 key)
Rate of return = 13.92%

Question 32

Calculate the weighted-average expected return and the weighted beta coefficient for his current portfolio.

50k invested in Growth Mutual Fund. Beta = 1.3, Expected return 15%.
30k invested in Stock MNY. Beta .7, Expected return: 10%

Answer 32

Expected Return:
15 Input
50,000 Σ+
10 Input
30,000 Σ+
SHIFT ⎯xw (6 key)
Rate of return = .13125 = 13.125%

Weighted beta coefficient:
1.3 Input
50,000 Σ+
.7 Input
30,000 Σ+
SHIFT ⎯xw (6 key)
Weighted beta = 1.075

Question 33

Calculate the weighted-average expected return and the weighted beta coefficient for his current portfolio.

60k invested in Growth Mutual Fund. Beta = 1.3, Expected return 15%.

Stock PQZ, which has a beta of 1.0 and an expected return of 12%. If he decides to buy Stock PQZ, he will invest $20,000

Answer 33

.15 Input
60,000 Σ+
.12 Input
20,000 Σ+
SHIFT ⎯xw (6 key)
Rate of return = .1425 = 14.25%

1.3 Input
60,000 Σ+
1 Input
20,000 Σ+
SHIFT ⎯xw (6 key)
Weighted beta = 1.225

Question 34

Calculate the standard deviation and mean return for the following individual securities:
yr. 1: 8%, yr. 2: 10%, yr. 3: 12%, yr. 4: 14%

Answer 34

8 Σ+
10 Σ+
12 Σ+ 
14 Σ+
HP-10BII+ (set for 1 P/Yr): standard deviation: SHIFT, SxSy (8 key) = 2.5820

Mean return: SHIFT, x, y (7 key) = 11.00

Question 35

The Stargazer Fund has a mean (average) return of 10%, and a standard deviation of 15%. Assuming the returns are normally distributed, what range of returns would you expect

Answer 35

68% of the time?
–5% to +25% (10 – 15 = –5, and 10 + 15 = 25)
95% of the time?
–20% to +40% (–5 – 15 = –20, and 25 + 15 = 40)
99% of the time?
–35% to +55% (–20 – 15= –35 and 40 + 15 = 55)

Question 36

Scorpio Inc. has a mean return of 19%, and a standard deviation of 25. What is the probability that the stock will have a return greater than 19% if the returns are normally distributed?

Answer 36

The answer is 50%. In a normally distributed yield curve, half of the returns will be greater than the mean return, and half of the returns will be less than the mean return.

Question 37

Libra Inc. has a mean return of 11%, and a standard deviation of 9. Assuming the returns are normally distributed, what is the probability that the stock will have a return greater than 20%?

Answer 37

The answer is 16%. We know that half of the returns are going to be greater than the mean return of 11%. We also know that one standard deviation (which will be evenly distributed) accounts for 68% of the returns and would range from +2% to +20%. Half of the 68% of returns would be above the mean return, and half below. So 34% of the returns would be greater than the 11% mean return, and would fall between 11% and 20%.If we know 50% of the returns will be greater than 11%, and we know that 34% of the returns will fall between 11% and 20%, we then know that 16% (what remains of the 50%, 50 – 34) of the returns will be greater than 20%.

Question 38

What does semi-variance measure?

Answer 38

Semi-variance measures only the returns that fall below the average, and is primarily used by portfolio managers. It recognizes that investors are concerned less about upside potential and more about downside risk.

Question 39

Using the possible expected annual returns given below for two stocks, calculate the standard deviation, mean return, and coefficient of variation for each stock. Which stock would you choose and why?

Stock A:
YR1: 6%; YR2: 8%, YR3: 10%, YR4: 12%

Stock B:
YR1: 8%, YR2 9%, YR3: 9.25%, YR4: 9.5%

Answer 39

Stock A:
6
Σ+
8
Σ+
10
Σ+
12
Σ+
Average (Mean) return = SHIFT ⎯ x, ⎯y (7 key) = 9.0%
Standard deviation = SHIFT, Sx, Sy (8 KEY) = 2.5820

Coefficient of Variation: Standard Deviation (S) divided by the mean: 2.582/9= .287

Stock B: 
8
Σ+
9
Σ+
9.25
Σ+
9.5
Σ+
Average (Mean) return = SHIFT, ⎯x, ⎯y (7 key) = 8.9375
Standard deviation = SHIFT, Sx, Sy (8 key) = .6575

Coefficient of Variation: Standard Deviation (S) divided by the mean: .6575/8.9375= .07357

Stock A has a coefficient of variation of .29, and Stock B has a coefficient of variation of .07. Choose the lower number, so we would select Stock B, since it has less risk per unit of return.

Question 40

Briefly describe covariance, and its importance in constructing a well- diversified portfolio.

Answer 40

Covariance measures how much two investments are related to each other; in other words, how much they move together or apart.

• The lower the covariance, the lower the correlation between the two assets, and the more diversification we achieve.
• As we add additional assets to a portfolio, we want to make sure they are not highly correlated with the assets we already own.
• Covariance can be just about any number, so it can be difficult to understand the correlation.
• There is a standardized form of covariance that is easier to work with and understand, since it confines the correlation between –1 and +1, and this is called the correlation coefficient.

Question 41

The standard deviation of the market is 14, and the standard deviation of United Enterprises Inc. is 22. The correlation coefficient between the two is .85. What is their covariance?

Answer 41

COVij =ρij σi σj
COVij = 14 ×22×.85
COVij = 261.80

Question 42

What is the coefficient of variation?

Answer 42

A statistical measure of the relative dispersion of data points around the mean.

Coefficient of variation is one of the methods for computing a risk-adjusted return for a security. For example, investors that know both the standard deviation and mean return for two or more securities can calculate the coefficient of variation for each security. Then, rather than simply selecting the security that has the greatest absolute return or the lowest absolute risk over the period measured, an investor can use the coefficient of variation to determine which security gave the least risk per unit of return.

Another way to look at it is that the higher the number, the more risk per unit of return, and the lower the number, the less risk per unit of return

Question 43

What is the correlation coefficient?

Answer 43

The correlation coefficient standardizes covariance for us, and puts boundaries of –1 and +1 on the relationship of two assets. It is R.

Question 44

What is covariance?

Answer 44

Covariance measures the extent to which two variables (such as two stocks) are related to each other, or how the price movements of one of the securities are related to the price movements of a second security.

Question 45

The covariance between Twin Pines Inc. and the S&P 500 is 95. The standard deviation of Twin Pines is 13, and the market’s standard deviation is 12. What is their correlation coefficient?

Answer 45

Rij = COVij/ σi ×σj
Rij= 95/ 13 x 12
Rij = .6090

(The 95 has to be divided by the total of the numbers multiplied (13 x 12).

Question 46

What is the formula for correlation coefficient?

Answer 46

Rij = COVij /σi ×σj

Question 47

What does CV stand for?

Answer 47

coefficient of variation

Question 48

What is the formula for Coefficient of Variation (CV)

Answer 48

CV = S/Mean

S= standard deviation
Mean= Average returns

Question 49

Consider the following information concerning stocks F and G. The covariance between stocks F and G is –22.

STOCK F: Expected Return: 9%; Standard Deviation: 7
STOCK G: Expected Return: 14%; Standard Deviation: 16

What is the expected return of a portfolio that has 40% invested in Stock F and 60% invested in Stock G?

Answer 49

.40 × 9% = 3.6%
.60 × 14% = 8.4%
3.6% + 8.4% = 12.0% expected return

Question 50

Consider the following information concerning stocks F and G. The covariance between stocks F and G is –22.

STOCK F: Expected Return: 9%; Standard Deviation: 7
STOCK G: Expected Return: 14%; Standard Deviation: 16

What is the standard deviation of a portfolio containing these two stocks in the percentages indicated (40% invested in Stock F and 60% invested in Stock G)?

Answer 50

S= square root of Wf2Sf2+Wg2Sg2+2WfWgCOV fg

Sp= (.4)2(7)2+(.6)2(16)2+2(.4)(.6)(-22)=9.5

Question 51

Consider the following information concerning stocks F and G. The covariance between stocks F and G is –22.

STOCK F: Expected Return: 9%; Standard Deviation: 7
STOCK G: Expected Return: 14%; Standard Deviation: 16

What are the correlation coefficient and coefficient of determination of Stock F and Stock G?

Answer 51

Rfg= -22/(7)x(16) = -.2

Rfg squared= (-.2) x (-.2) = .04

Question 52

Calculate the coefficient of determination, given the following correlation coefficients between an asset and a benchmark:

1.00 0.95 0.80 0.50 0.23

Answer 52

Converting the correlation coefficient (R) to the Coefficient of Determination (R2 or R-squared) just requires squaring the correlation coefficient. You can simply multiply R by itself, or use the following keystrokes:
Example: Correlation Coefficient of .95:

Correlation Coefficient (R)
Coefficient of Determination (R2)

Example for .95
HP-10BII+
.95 SHIFT
X squared` (the “+” key) Solution: .9025

Question 53

Calculate the correlation coefficient, given the following coefficient of determinations between an asset and a benchmark.
.98 .86 .70 .50 .04

Answer 53

When converting the coefficient of determination into the correlation coefficient, we are taking the square root of the coefficient of determination (going the other way we square the correlation coefficient).

Example: Coefficient of determination of .86:
.86
shift: (the “–” key)
Solution: .9274

Question 54

What is: Coefficient of Determination (R-squared)

Answer 54

R2 indicates the percentage of one asset’s movement that can be explained by the movement of a second asset. Generally, the second asset is a market index or benchmark, such as the S&P 500 index, and the first asset is an individual stock or a mutual fund.

Question 55

What does the coefficient of determination (R2) tell us about systematic and unsystematic risk?

Answer 55

The coefficient of determination (R2) tells us how much of the risk is explained by the benchmark. For example, if we are comparing the Titanic Fund to the S&P 500, and the coefficient of determination is .70, this would mean that 70% of the price movement of the Titanic Fund is explained by the S&P 500 (systematic risk), and the other 30% is not explained by the S&P 500 Index (unsystematic risk). For diversification purposes, the lower the coefficient of determination (and thus the correlation coefficient) the better. However, beta is a measure of systematic risk, and since the coefficient of determination (R2) is a measure of systematic risk, when using beta the higher the coefficient of determination (R2), the better

Question 56

1. Answer the following questions about beta.
   a. Compute beta for the following five sets of facts.

1 standard deviation 30, market 15; correlation coefficient: 1.0
2 standard deviation 30, market 15; correlation coefficient: .25
3 standard deviation 30, market 15; correlation coefficient: 0
4 standard deviation 30, market 15; correlation coefficient: -.25
5 standard deviation 30, market 15; correlation coefficient: -1.0

Answer 56

β=Si /Sm x Rim

(1) 30/15 × 1.0 = 2.0
(2) 30/15 × +0.25 = +0.5
(3) 30/15 × 0.0 = 0.0
(4) 30/15 × –0.25 = –0.5
(5) 30/15 × –1.0 = –2.0

Question 57

What is the significance of correlation coefficient to the accurate interpretation of the meaning of beta?

Answer 57

Beta is significant if properly calculated. Intuitively, an investor might conclude that a stock with a standard deviation that is twice the standard deviation of the market would have a beta of 2.0. The computations show that to be the case only when the stock in question is highly correlated with the market. Even with a low positive correlation (+0.25), the beta is only 0.5. Many investors will conclude that a stock with a beta of 0.5 is half as variable as the market; what this computation should actually tell them is that they cannot use beta to judge the volatility of the stock, but instead must refer to the stock’s standard deviation to measure the volatility of the stock. Beta cannot be accepted blindly without knowing how the stock in question is correlated with the market index against which its beta is calculated.

Question 58

What is the approximate price movement of the following assets, given the following betas, and a market return of +15%?
Beta: 1.4; market change 15%

Answer 58

Simply multiply the beta times the market change.

Question 59

Assuming that the correlation of a stock and the market is high, what would beta coefficients of 0.5, 1.0, and 1.5 mean to someone investing in the stock?

Answer 59

The larger the beta coefficient is, the more volatile the security’s historic price is relative to the market. Investors often use beta as a rule of thumb for estimating the percentage change in a stock’s price when the overall market moves X%. A beta of 1.0 indicates the movement of the stock would be expected to be identical to the movement of the market. A beta of 0.5 means that the price of the stock has been less volatile than the market; for example, if the overall market changes by 4%, the stock would be expected to change by 2%. If a stock has a beta of 1.5, the price on the stock would be expected to change by 6% when the market changes by 4%. Stocks with high beta coefficients are referred to as “aggressive,” while stocks with low beta coefficients are referred to as “defensive.”

Question 60

What is the required return for the following securities? The risk-free rate is 4%, and the market return is 8%.

Triad Industries Beta: 0.9

Answer 60

Triad Industries: 4 + (8 – 4) 0.9 = 4 + 3.60 = 7.60

Question 61

What is the term used for the difference between the market return and the risk-free rate (Rm – Rf)?

Answer 61

This is called the “market risk premium.” It is the excess return earned above the risk-free rate to compensate the investor for taking extra risk by investing in the market. There is much discussion and disagreement over what the future market risk premium will be.

Question 62

What is the appropriate Treasury security to use for the risk free rate?

Answer 62

The most widely used Treasury security is the three-month Treasury bill, and this is what is favored by the CFP Board for the exam. However, some portfolio managers use the five-year or ten-year Treasury note since stocks are a long-term investment, and the investor’s holding period is often five or ten years, or longer.

Question 63

What is the long-term historical market risk premium in the United States?

Answer 63

The long-term historical market risk premium in the United States, from 1926–2015, has been 6.6%.

Question 64

Assume that the following securities have the standard deviations and covariances as shown.

A: Standard Deviation: 15.2
B: Standard Deviation: 10.6
AB Covariance: 74

Compute the correlation coefficient (R) and the coefficient of determination (R2) for stocks A/B,

Answer 64

Rab= 74/(15.2) x(10.6)= .459

Question 65

Constructing a systematically developed portfolio requires paying attention to which two factors?

Answer 65

• Eliminating unsystematic risk.

- Minimizing the total risk, which is measured by standard deviation.

Question 66

An investor has an index mutual fund, and adds an actively managed fund that has an R2 of .94 with the index fund. Has the investor effectively diversified? Why or why not?

Answer 66

The amount of diversification that would be achieved in this case is minimal. 94% of the price movement of the actively managed fund is explained by the index mutual fund the investor already holds. This means that the actively managed fund will essentially mirror the performance of the index fund. The investor would be better off looking for a fund that has a lower R2 to the index fund. For diversification purposes, the lower the R2 the better.

Question 67

correlation coefficient is sometimes referred to as:

Answer 67

R

Question 68

coefficient of determination is referred to as:

Answer 68

“R-squared”